# Determine the product of the following factors:?

(1-1/2)(1-1/3)(1-1/4)...(1-1/98)(1-1/99)(1-1/100). Those dots ar the elipses there are numbers in between there just too much to write out but follows the same pattern.

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- Anonymous9 years agoBest Answer
Do the subtraction of the fractions in each term to get

(1/2) (2/3) (3/4) (4/5) ... (98/99)

Notice that you can rewrite this product as:

(1*2*3*4* ... * 98) / (2*3*4* ... * 98*99)

So most of these terms cancel each other out, leaving you with 1/99.

If you tried doing this with a calculator, it would not only take you hours, but your answer would probably be wrong with all of the decimal round-off error building up.

Source(s): BS & MS in mathematics - TheSicilianSageLv 79 years ago
.............. n

Product = Π (1 - 1/k) = 1/n; Lim n→∞ Product → 0

.............. k=2

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